A pattern-theoretic characterization of biological growth

Spatiotemporal Cardiac Statistical Shape Modeling: A Data-Driven Approach

Clinical investigations of anatomy's structural changes over time could greatly benefit from population-level quantification of shape, or spatiotemporal statistic shape modeling (SSM). Such a tool enables characterizing patient organ cycles or disease progression in relation to a cohort of interest. Constructing shape models requires establishing a quantitative shape representation (e.g., corresponding landmarks). Particle-based shape modeling (PSM) is a data-driven SSM approach that captures population-level shape variations by optimizing landmark placement. However, it assumes cross-sectional study designs and hence has limited statistical power in representing shape changes over time. Existing methods for modeling spatiotemporal or longitudinal shape changes require predefined shape atlases and pre-built shape models that are typically constructed cross-sectionally. This paper proposes a data-driven approach inspired by the PSM method to learn population-level spatiotemporal shape changes directly from shape data. We introduce a novel SSM optimization scheme that produces landmarks that are in correspondence both across the population (inter-subject) and across time-series (intra-subject). We apply the proposed method to 4D cardiac data from atrial-fibrillation patients and demonstrate its efficacy in representing the dynamic change of the left atrium. Furthermore, we show that our method outperforms an image-based approach for spatiotemporal SSM with respect to a generative time-series model, the Linear Dynamical System (LDS). LDS fit using a spatiotemporal shape model optimized via our approach provides better generalization and specificity, indicating it accurately captures the underlying time-dependency.

Predictive Statistical Model of Early Cranial Development

OBJECTIVE

We present a data-driven method to build a spatiotemporal statistical shape model predictive of normal cranial growth from birth to the age of 2 years.

METHODS

The model was constructed using a normative cross-sectional computed tomography image dataset of 278 subjects. First, we propose a new standard representation of the calvaria using spherical maps to establish anatomical correspondences between subjects at the cranial sutures - the main areas of cranial bone expansion. Then, we model the cranial bone shape as a bilinear function of two factors: inter-subject anatomical variability and temporal growth. We estimate these factors using principal component analysis on the spatial and temporal dimensions, using a novel coarse-to-fine temporal multi-resolution approach to mitigate the lack of longitudinal images of the same patient.

RESULTS

Our model achieved an accuracy of 1.54 ± 1.05 mm predicting development on an independent longitudinal dataset. We also used the model to calculate the cranial volume, cephalic index and cranial bone surface changes during the first two years of age, which were in agreement with clinical observations.

SIGNIFICANCE

To our knowledge, this is the first data-driven and personalized predictive model of cranial bone shape development during infancy and it can serve as a baseline to study abnormal growth patterns in the population.

Shape from Contour: Computation and Representation

The human visual system reliably extracts shape information from complex natural scenes in spite of noise and fragmentation caused by clutter and occlusions. A fast, feedforward sweep through ventral stream involving mechanisms tuned for orientation, curvature, and local Gestalt principles produces partial shape representations sufficient for simpler discriminative tasks. More complete shape representations may involve recurrent processes that integrate local and global cues. While feedforward discriminative deep neural network models currently produce the best predictions of object selectivity in higher areas of the object pathway, a generative model may be required to account for all aspects of shape perception. Research suggests that a successful model will account for our acute sensitivity to four key perceptual dimensions of shape: topology, symmetry, composition, and deformation.

Frequency tuning of shape perception revealed by classification image analysis

Classification image analysis is a powerful technique for elucidating linear detection and discrimination mechanisms, but it has primarily been applied to contrast detection. Here we report a novel classification image methodology for identifying linear mechanisms underlying shape discrimination. Although prior attempts to apply classification image methods to shape perception have been confined to simple radial shapes, the method proposed here can be applied to general 2-D (planar) shapes of arbitrary complexity, including natural shapes. Critical to the method is the projection of each target shape onto a Fourier descriptor (FD) basis set, which allows the essential perceptual features of each shape to be represented by a relatively small number of coefficients. We demonstrate that under this projection natural shapes are low pass, following a relatively steep power law. To efficiently identify the observer's classification template, we employ a yes/no paradigm and match the spectral density of the stimulus noise in FD space to the power law density of the target shape. The proposed method generates linear template models for animal shape detection that are predictive of human judgments. These templates are found to be biased away from the ideal, overly weighting lower frequencies. This low-pass bias suggests that higher frequency shape processing relies on nonlinear mechanisms.

A discriminative feature selection approach for shape analysis: Application to fetal brain cortical folding

The development of post-processing reconstruction techniques has opened new possibilities for the study of in-utero fetal brain MRI data. Recent cortical surface analysis have led to the computation of quantitative maps characterizing brain folding of the developing brain. In this paper, we describe a novel feature selection-based approach that is used to extract the most discriminative and sparse set of features of a given dataset. The proposed method is used to sparsely characterize cortical folding patterns of an in-utero fetal MR dataset, labeled with heterogeneous gestational age ranging from 26 weeks to 34 weeks. The proposed algorithm is validated on a synthetic dataset with both linear and non-linear dynamics, supporting its ability to capture deformation patterns across the dataset within only a few features. Results on the fetal brain dataset show that the temporal process of cortical folding related to brain maturation can be characterized by a very small set of points, located in anatomical regions changing across time. Quantitative measurements of growth against time are extracted from the set selected features to compare multiple brain regions (e.g. lobes and hemispheres) during the considered period of gestation.

A Stochastic Approach to Diffeomorphic Point Set Registration with Landmark Constraints

This work presents a deformable point set registration algorithm that seeks an optimal set of radial basis functions to describe the registration. A novel, global optimization approach is introduced composed of simulated annealing with a particle filter based generator function to perform the registration. It is shown how constraints can be incorporated into this framework. A constraint on the deformation is enforced whose role is to ensure physically meaningful fields (i.e., invertible). Further, examples in which landmark constraints serve to guide the registration are shown. Results on 2D and 3D data demonstrate the algorithm's robustness to noise and missing information.

Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data

This paper proposes an original approach for the statistical analysis of longitudinal shape data. The proposed method allows the characterization of typical growth patterns and subject-specific shape changes in repeated time-series observations of several subjects. This can be seen as the extension of usual longitudinal statistics of scalar measurements to high-dimensional shape or image data. The method is based on the estimation of continuous subject-specific growth trajectories and the comparison of such temporal shape changes across subjects. Differences between growth trajectories are decomposed into morphological deformations, which account for shape changes independent of the time, and time warps, which account for different rates of shape changes over time. Given a longitudinal shape data set, we estimate a mean growth scenario representative of the population, and the variations of this scenario both in terms of shape changes and in terms of change in growth speed. Then, intrinsic statistics are derived in the space of spatiotemporal deformations, which characterize the typical variations in shape and in growth speed within the studied population. They can be used to detect systematic developmental delays across subjects. In the context of neuroscience, we apply this method to analyze the differences in the growth of the hippocampus in children diagnosed with autism, developmental delays and in controls. Result suggest that group differences may be better characterized by a different speed of maturation rather than shape differences at a given age. In the context of anthropology, we assess the differences in the typical growth of the endocranium between chimpanzees and bonobos. We take advantage of this study to show the robustness of the method with respect to change of parameters and perturbation of the age estimates.

A feature-based developmental model of the infant brain in structural MRI

In this paper, anatomical development is modeled as a collection of distinctive image patterns localized in space and time. A Bayesian posterior probability is defined over a random variable of subject age, conditioned on data in the form of scale-invariant image features. The model is automatically learned from a large set of images exhibiting significant variation, used to discover anatomical structure related to age and development, and fit to new images to predict age. The model is applied to a set of 230 infant structural MRIs of 92 subjects acquired at multiple sites over an age range of 8-590 days. Experiments demonstrate that the model can be used to identify age-related anatomical structure, and to predict the age of new subjects with an average error of 72 days.

A nonconservative Lagrangian framework for statistical fluid registration-SAFIRA

In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented , where the deformation was regularized by penalizing deviations from a zero rate of strain. In , the terms regularizing the deformation included the covariance of the deformation matrices (Σ) and the vector fields (q) . Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies.